Find the equation of the tangent to a parabola $\displaystyle y^2=4ax$ at the given pt $\displaystyle (x_1,y_1)$ on it. What can you say about the tangent at $\displaystyle (0,0)$?

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- Dec 23rd 2008, 01:28 AMvarunnayuduFinding eq of tangent to a parabola.
Find the equation of the tangent to a parabola $\displaystyle y^2=4ax$ at the given pt $\displaystyle (x_1,y_1)$ on it. What can you say about the tangent at $\displaystyle (0,0)$?

- Dec 23rd 2008, 03:10 AMIsomorphism
Just apply the definition for the first part:

$\displaystyle y - y_1 = \frac{dy}{dx}\bigg{|}_{x = x_1, y = y_1} (x - x_1)$

If $\displaystyle y_1 \neq 0, y - y_1 = \frac{2a}{y_1} (x - x_1)$

$\displaystyle y_1 y - y_1 ^2 = 2ax - 2ax_1$

If $\displaystyle y_1 = 0$, then $\displaystyle x_1 = 0$ and the tangent is the y - axis. - Dec 30th 2008, 08:58 PMzorrothanks
thanks man